Extensions 1→N→G→Q→1 with N=C₅ and Q=C₅⋊D₄

Direct product G=N×Q with N=C₅ and Q=C₅⋊D₄

		d	ρ	Label	ID
C₅×C₅⋊D₄		20	2	C5xC5:D4	200,31

Semidirect products G=N:Q with N=C₅ and Q=C₅⋊D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₅⋊D₄) = C₅⋊D₂₀	φ: C₅⋊D₄/Dic₅ → C₂ ⊆ Aut C₅	20	4+	C5:1(C5:D4)	200,25
C₅⋊₂(C₅⋊D₄) = C₅²⋊₂D₄	φ: C₅⋊D₄/D₁₀ → C₂ ⊆ Aut C₅	40	4-	C5:2(C5:D4)	200,24
C₅⋊₃(C₅⋊D₄) = C₅²⋊₇D₄	φ: C₅⋊D₄/C₂×C₁₀ → C₂ ⊆ Aut C₅	100		C5:3(C5:D4)	200,36

Non-split extensions G=N.Q with N=C₅ and Q=C₅⋊D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₅⋊D₄) = C₂₅⋊D₄	φ: C₅⋊D₄/C₂×C₁₀ → C₂ ⊆ Aut C₅	100	2	C5.(C5:D4)	200,8

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C5 and Q=C5⋊D4